p.3 polynomials and special products
DESCRIPTION
P.3 Polynomials and Special Products. Unit P:Prerequisites for Algebra 5-Trig. Definition of a Polynomial in x. Let a 0 , a 1 , a 2 , …, a n be real numbers and let n be a nonnegative integer. A polynomial in x is an expression of the form a n x n + a n-1 x n-1 + … + a 1 x + a 0 - PowerPoint PPT PresentationTRANSCRIPT
Definition of a Polynomial in x
• Let a0, a1, a2, …, an be real numbers and let n be a nonnegative integer. A polynomial in x is an expression of the form
anxn + an-1xn-1 + … + a1x + a0
where an ≠ 0. The polynomial is of degree n, an is the leading coefficient, and a0 is the constant term.
Operations with Polynominials
• You can add and subtract polynomials by combining like terms.
• To find the product you must distribute.
Special Products
• Sum and Difference of Same Terms• (a + b)(a – b) = a2 – b2
• Square of a Binomial• (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 – 2ab + b2
• Cube of a Binomial• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a – b)3 = a3 – 3a2b + 3ab2 – b3